They mean the same thing. Very slightly different connotations, though.

I believe a person is dumb when they do something wrong and don't even realize it's wrong. Stupid is when you do it on purpose. Dumb: Biologically incapable to think, They can also be called as abnormal. Should not be insulted. They do not know what they do. Stupid: Lacking or marked by lack of intellectual acuity .Should be maltreated because they do not apply any logic in everything they do.Should be insulted.